Question

Each of the four angles of rectangle is a right angle prove

Answer 1

Answer:

Step-LET ABC BE A RECTANGLE IN WHICH ANGLE A =90 DEGREE WE HAVE TO SHOW THAT ANGLE B= ANGLE C= ANGLE D=90 DEGREE WE HAVE AD // BC AND AB IS A TRANSVERSAL SO, ANGLE A + ANGLE B = 180 DEGREE(INTERIOR ANGLES ON THE SAME SIDE OF THE TRANSVERSAL0 BUT, ANGLE A =90 DEGREE SO, ANGLE B = 180 - ANGLE A = 180 - 90 = 90 DEGREE ANGLE C= ANGLE A AND ANGLE D= ANGLE B (OPPOSITE ANGLES OF THE //GM) SO, ANGLE C=90 AND ANGLE D=90 THEREFORE, EACH OF THE ANGLES OF A RECTANGLE IS 90 DEGREE. HENCE,PROVED

Answer 2

${\huge{\underline{\underline{\sf{\pink{Solutions:-}}}}}}$

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${\large{\underline{\underline{\sf{\red{Given:-}}}}}}$ A rectangle ABCD such that ∠A =90°

${\large{\underline{\underline{\sf{\green{To\:Prove:-}}}}}}$ ∠A =∠B=∠C=∠D= 90°

${\large{\underline{\underline{\sf{\blue{Answer:-}}}}}}$ ABCD is a rectangle

➡ ABCD is a parallelogram

➡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀AB || BC

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀AD || BC and line AB intersects them at Aand B.

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ∠A + ∠B = 180°

⠀⠀⠀[ Sum of the interior angles on the same side of a tranversal is 180°]

➡ 90° + ∠B = 180° ⠀⠀⠀⠀⠀⠀⠀[∠A = 90°(Given)]

➡ ∠B = 90°

Similarly, we can show that∠C = 90°and∠D =90°

${\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>{\underline{\underline{\sf{\</strong><strong>p</strong><strong>i</strong><strong>n</strong><strong>k</strong><strong>{</strong><strong>H</strong><strong>e</strong><strong>n</strong><strong>c</strong><strong>e</strong><strong>,</strong><strong>:-}}}}}}$ ∠A =∠B=∠C=∠D= 90°

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